A community for students.
Here's the question you clicked on:
 0 viewing
jonnymiller
 3 years ago
Hi all, I am still working on second derivative tests having trouble with finding the critical points.
The problem is find the critical points of f(x,y)=sinx+siny+cos(x+y) for x between 0 and pie/4 and y between 0 and pie/4. Classify each as a local min, max, or saddle point.
f(x,y)=sinx+siny+cos(x+y)
I found the partials to be:
derivative of f with respect to x = fx=cosxsin(x+y)
derivative of f with respect to y = fy=cosysin(x+y)
I am having trouble solving the partials for 0.
jonnymiller
 3 years ago
Hi all, I am still working on second derivative tests having trouble with finding the critical points. The problem is find the critical points of f(x,y)=sinx+siny+cos(x+y) for x between 0 and pie/4 and y between 0 and pie/4. Classify each as a local min, max, or saddle point. f(x,y)=sinx+siny+cos(x+y) I found the partials to be: derivative of f with respect to x = fx=cosxsin(x+y) derivative of f with respect to y = fy=cosysin(x+y) I am having trouble solving the partials for 0.

This Question is Closed

jonnymiller
 3 years ago
Best ResponseYou've already chosen the best response.0For fx=cosxsin(x+y)=0 fy=cosysin(x+y)=0 x=pie/6 y=pie/6 I did this by trial and error. Does anyone know how to solve it algebraically?

bbnl1990
 3 years ago
Best ResponseYou've already chosen the best response.1First, eliminate sin(x+y): fxfy=0 cos(x)cos(y)=0 cos(x)=cos(y) x=y Plug x=y to either fx or fy: fx=cos(y)sin(y+y)=0 cos(y)=sin(2y) cos(y)=cos(pi/22y) y=(pi/2)2y 3y=pi/2 y=pi/6 Since x=y, x=pi/6

jonnymiller
 3 years ago
Best ResponseYou've already chosen the best response.0Very clever!! That makes a lot of sense!! It's amazing how easy it looks once you've seen it done. I have been puzzling over that one for days! Thanks!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.